The lack of reliability of previous methods let us esperate
to reach better accuracy taking into acount the evolution of box center
values of Tadim and V during iteration process.On the graph just below, we can see that after a transient
evolution, Tadim and V reach a levelled state.To determine the critical Ra number using Tadim curves,
we use the same preceeding idea that is Tadim should yields to 0.5 for
critical and under-critical Ra.To determine the critical Ra number using V curves, we
use the idea that V should yields to 0 for critical and under-critical
Ra.

Firstly choose
an arbitrary over-critical Ra number. e.g.~1850. Then produce a series
of curves with decreasing Ra. We can then determine a major boundary
value for the Rac. On the graph below it is clear that : Rac
<1758 (grey curve) For an accurate determination we must
zoom
to low speeds area.

Box center vertical velocity

Zoom to low
speeds area:

We plot curves with decreasing Ra number up to reach a
value of Ra for which the mean value of the velocity is about null. We
have reached the 1589 Ra number.Themain problem of this type of determination
is the difficulty to say if the mean value of the velocity curve can be
considered as 0.If the curves are well ordered ,i.e. the mean value of
the velocity deacreases with Ra number, we can then obtain a more accurate
result.Looking at the graph we can say that 1589< Rac
<1711 i.e. Rac = 1650 +/-60.Nevertheless the monotonic placement of the red, green
and blue curves let us to say that Rac ~1711.It should be noticed that the differenciation
between curves near critical Ra number becomes more and more diffcult as
the mesh is finer.

Box center vertical velocity

2) Determination of Rac using
Tadim.

A seek to next
graph let see that for critical and under-critical Ra numbers Tadim does
not tend to 0.5 but to 0.45. This problem comes from the manner of FLUENT
to interpolate temperature at a point when this point does not match with
a grid point. No matter this artificial shifting value effect the user
will compute a far under-critical Ra number simulation to get the limit
value of Tadim. Here it is 0.452.

The observation
of the set of Tadim curves yields to the same conclusion as done studying
V : We can then determine a major boundary value for the Rac.
On the graph below it is clear that : Rac <1758 (grey curve) For an accurate determination we must
zoom
to low speeds area.

Box center dimensionless temperature

Zoom to low
speeds area:

We can see that the determination of critical Ra
number is more difficult tham with V , since the curves placement is not
monotonic.Looking at the graph we can say that 1589< Rac
<1753 i.e. Rac = 1671 +/-80It should be noticed that the differenciation
between curves near critical Ra number becomes more and more diffcult as
the mesh is finer.

Box center dimensionless temperature

3) Conclusion

At first, we noticed that the determination of Rac
is less accurate using Tadim than with V.The use of these methods should leads to some problems
of accuracy for fine meshes because of the difficulty to separate curves
behaviors.